1. Field of the Invention
The present invention relates to a stigmator assembly for correcting astigmatism produced in an instrument using a charged-particle beam such as a transmission electron microscope and, more particularly, to a stigmator assembly capable of correcting even three-fold astigmatism.
2. Description of the Related Art
With respect to on-axis astigmatism due to parasitic aberration in a transmission electron microscope, the first-order on-axis astigmatism shows a two-fold symmetry from a viewpoint of geometrical optics, while the second-order on-axis astigmatism shows a three-fold symmetry. Generally, an electron microscope is equipped with an octopole coil assembly for introducing a quadrupole field in the plane of the opening to correct astigmatism with a two-fold symmetry (hereinafter referred to as two-fold astigmatism). The exciting currents through the coils are controlled to produce a magnetic field for canceling the two-fold astigmatism.
Since the effect of astigmatism with a three-fold symmetry (hereinafter referred to as three-fold astigmatism) on the image is smaller than second-fold astigmatism, the necessity of correction of three-fold astigmatism has not been great. However, installation of a field emission gun or the like has increased the response characteristics of the electron microscope relative to the spatial frequency. Where such improved response characteristics are taken into consideration, image distortion due to three-fold astigmatism can no longer be neglected.
Generation of three-fold astigmatism and its correction are hereinafter described briefly. In an electromagnetic lens, the magnetic potential has slight deviation from axial symmetry. The deviation is caused by the fact that the bore in the polepieces forming the potential is not perfectly circular. In a cylindrical coordinate system (r, xcex8, z), expanding an arbitrary potential xcfx86 into Fourier components (Am (r, z), Bm (r, z)) with respect to xcex8 gives rise to                     φ        =                              ∑                          (                                                                                          A                      m                                        ⁡                                          (                                              r                        ,                        z                                            )                                                        ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          m                      ⁢                                              xe2x80x83                                            ⁢                      θ                                        )                                                  +                                                                            B                      m                                        ⁡                                          (                                              r                        ,                        z                                            )                                                        ⁢                  sin                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          m                      ⁢                                              xe2x80x83                                            ⁢                      θ                                        )                                                              )                                m                                    (        1        )            
Expansion into Fourier components in the cylindrical coordinate system (r, xcex8, z) is known as multiple magnetic field expansion.
Generally, terms other than axially symmetrical components appear in xcfx86 (r, xcex8, z) and induce different kinds of parasitic aberrations. The effects of disordered deviation from axial symmetry can be expressed as a combination of aberrations corresponding to multiple poles that are expanded terms. For the sake of simplicity of illustration, it is assumed that uniformity is achieved in the z-direction. Of the expanded components, the aberration induced by a potential given by Eq. (2) is considered.
xcfx863=C3r3 cos 3(xcex83xe2x88x92xcex8)xe2x80x83xe2x80x83(2) 
In Eq. (2), C3 indicates the amount of potential, and xcex83 indicates the phase of the potential. Examples of distribution of xcfx863 are shown in FIG. 5, where distributions of xcfx863=1 and xcfx863=xe2x88x921 are shown under the condition where C3=1 and xcex83=0. In FIG. 5, the circle inscribing the curves has r=1. Let B be a magnetic field derived from the potential given by Eq. (2). As shown in the potential curves of FIG. 5, the magnetic field B in this case is a hexapole field owing to a hexapole. Using (r, xcex8) coordinates, the magnetic field B is given by                                                         B              =                                                -                                      u                    0                                                  ⁢                                  ∇                                      φ                    3                                                                                                                          =                                                -                                                            u                      0                                        ⁡                                          (                                                                                                    ∂                                                          xe2x80x83                                                                                                            ∂                            r                                                                          ,                                                                              1                            r                                                    ⁢                                                                                    ∂                                                              xe2x80x83                                                                                                                    ∂                              θ                                                                                                                          )                                                                      ⁢                                  φ                  3                                                                                                        =                                                -                                      u                    0                                                  ⁢                                                      C                    3                                    ⁡                                      (                                                                  3                        ⁢                                                  r                          2                                                ⁢                        cos                        ⁢                                                  xe2x80x83                                                ⁢                        3                        ⁢                                                  (                                                                                    θ                              3                                                        -                            θ                                                    )                                                                    ,                                                                        -                          3                                                ⁢                                                  r                          2                                                ⁢                        sin                        ⁢                                                  xe2x80x83                                                ⁢                        3                        ⁢                                                  (                                                                                    θ                              3                                                        -                            θ                                                    )                                                                                      )                                                                                                          (        3        )            
The state of the magnetic field B on the circle inscribing the potential curves with xcex83=0 is indicated by the arrows in FIG. 6. The magnitude of the magnetic field B is constant on the circumference and is a quadratic function of r that does not depend on xcex8, as given by Eq. (4).
|B|=3C3xcexc0r2xe2x80x83xe2x80x83(4) 
If a round electron beam enters the magnetic field having the distribution as shown in FIG. 6 perpendicularly to the plane of the paper, the shape of the electron beam is distorted into a three-fold symmetry, i.e., rotational symmetry of 120xc2x0. This is three-fold astigmatism.
Of the deviation from the axially symmetrical components of the electromagnetic lens, the potential distribution as shown in FIG. 5 induces three-fold astigmatism. Therefore, in order to correct three-fold astigmatism, a potential distribution that cancels the astigmatism should be given close to the plane of opening of the electromagnetic lens. The r in Eq. (3) is made constant, and variation of xcex83 with varying xcex8 is shown in FIG. 7. This variation corresponds to variation in the potential on the circle inscribing the potential curves shown in FIGS. 5 and 6.
It is assumed that m coils Ln (n=1, 2, . . . , m) are placed on the circumference of the opening plane of the electromagnetic lens such that the coils are angularly regularly spaced from each other at intervals of T from xcex8=0 to correct three-fold astigmatism. Let LnIh be the ampere-turn of each coil necessary for the correction. The ampere-turn LnIh is the coil exciting currents corresponding to the potentials assigned to the coils, respectively, to form the corrective field. In FIG. 7, the potentials to be canceled by coils arranged under the conditions where xcex83=0, m=6, and T=xcfx80/3 are indicated by the broken lines. Generally, the ampere-turn LnIh is given by
LnIh=C3r3 cos 3(xcex83xe2x88x92nT)(T=2xcfx80/m)xe2x80x83xe2x80x83(5) 
Ideally, infinitesimal coils are placed consecutively (Txe2x86x920) to reproduce the distribution based on Eq. (3) and shown in FIG. 7. In reality, however, only one achievable method is to place a finite number of coils having finite dimensions. Even in this case, the exciting currents can be estimated using Eq. (5). Under the present situations, the coils are placed, taking account of points corresponding to the maximum value (C3r3) and the minimum value (xe2x88x92C3r3) in the distribution shown in FIG. 7. Six coils are necessary to create a hexapole field for correcting three-fold astigmatism. To rotate the magnetic field freely, 12 coils are generally placed.
As mentioned previously, three-fold astigmatism can be corrected by a stigmator in which 12 coils are positioned. However, in an electron microscope or the like, an octopole coil assembly has been already installed as some two-fold stigmators for correcting two-fold astigmatism. To correct three-fold astigmatism in an electron microscope, it is desired to place such stigmators in both illumination lens system and condenser lens system. If such stigmators are added under the condition where plural two-fold stigmators are installed, the height of the microscope column of the electron microscope is increased. Generally, limitations are placed on the height of a location where an electron microscope is installed. Where such limitations are taken into consideration, a three-fold stigmator may not be incorporated.
It is an object of the present invention to provide a stigmator assembly which comprises two-fold stigmators and a three-fold stigmator all mounted in an electron microscope, and capable of correcting even three-fold astigmatism, and having the same height as the conventional stigmator assembly having only two-fold stigmators.
A stigmator assembly in accordance with the present invention is equipped with plural stigmator coils circumferentially regularly spaced from each other on a circumference. The stigmator assembly further includes a control circuit for supplying sum control currents into the coils. The sum control currents are obtained by adding first control currents for producing a magnetic field that corrects three-fold astigmatism to second control currents for producing a magnetic field that corrects two-fold astigmatism.
Other objects and features of the invention will appear in the course of the description thereof, which follows.